58 



by shewing how his solution, given above> may be made to 

 produce a true result. Pie obtains the coefficients of P in 

 the increments of the abscissa and ordinate, from those of o, 

 and d', by an exceedingly ingenious process; having so de- 

 duced 0, and Qo— Ro^ — So^, &c. complete as far as P, he 

 exterminates o as before, and by a comparison of the co- 

 efficients (now correct) of ^^ he obtains the relation of gravity 

 and resistance. 



The ingenuity exhibited in the corrected solution is very 

 great, but it must be confessed that the solution is rather 

 prolix. The author concludes his corrected solution Avith 

 these words, Avhich may serve as an excuse for adding that 

 which concludes this paper. 



" Comme Newton n'est parvenu a ce dernier result, qu'en 

 suivant une marche analogue a celle du calcul differentiel, 

 nous avons cru qu'il n'etait pas inutile de faire voir 

 conmient la methode des series pouvait y conduire, et 

 qu'on nous saurait gre d'eclaircir, en meme temps un 

 point d'analyse sur lequel les plus grand geom^tres 

 s'etoient trompes, et qui pent interesser I'histoire de la 

 naissance des nouveaux calculs. 



THEOREM. 



